rsample::initial_split(Auto,prop = .5) -> Auto_split 

Auto_split

Auto_train <- rsample::training(Auto_split)

Auto_validation_set <- rsample::testing(Auto_split)

lm(mpg ~  poly(horsepower,3), Auto_train) -> trained_model

head(predict(trained_model, Auto_validation_set))

tibble(
    y = Auto_validation_set$mpg,
    y_hat = predict(trained_model, Auto_validation_set),
    resid_sqr = (y - y_hat)^2
) |>
    summarise(mse = mean(resid_sqr, na.rm = T))

# define a funciton

get_mse <- function(pow){

    # train the model - using trainging data
    lm(mpg ~ poly(horsepower,pow), Auto_train) -> trained_model

    # get mse
    tibble(
        y = Auto_validation_set$mpg,
        y_hat = predict(trained_model, Auto_validation_set),
        resid_sqr = (y - y_hat)^2
    ) |>
        summarise(mse = mean(resid_sqr, na.rm = T)) |>
        pull(mse) -> mse

    # Store appropriately

    tibble(
        pow_flexibility = pow,
        mse = mse
    )

}

map(
    c(1:10),
    get_mse
) |>
    list_rbind() |>
    ggplot(aes(pow_flexibility,mse))+
    geom_point()+
    geom_line()+
    labs(
    x = "Flexibility",
    y = "MSE"
    )+
    theme_minimal()

get_mse_spread <- function(pow){

    # repeats split for every iteration

    rsample::initial_split(Auto,prop = .5) -> Auto_split 

    Auto_train <- rsample::training(Auto_split)

    Auto_validation_set <- rsample::testing(Auto_split)

    # train the model - using trainging data
    lm(mpg ~ poly(horsepower,pow), Auto_train) -> trained_model

    # get mse
    tibble(
        y = Auto_validation_set$mpg,
        y_hat = predict(trained_model, Auto_validation_set),
        resid_sqr = (y - y_hat)^2
    ) |>
        summarise(mse = mean(resid_sqr, na.rm = T)) |>
        pull(mse) -> mse

    # Store appropriately

    tibble(
        pow_flexibility = pow,
        mse = mse
    )

    
}

map(
    rep(c(1:10),10) |> sort(),
    get_mse_spread
) |>
    list_rbind() |> 
    mutate(
        iteration = rep(letters[1:10],10)
    ) |>
    ggplot(aes(pow_flexibility,mse, colour = iteration))+
    geom_point()+
    geom_line(aes(group = iteration))+
    labs(
    x = "Flexibility",
    y = "MSE"
    )+
    theme_minimal() +
    theme(
        legend.position = "none"
    )

rsample::loo_cv(Auto) -> Auto_loocv_split

Auto_loocv_split

get_error_obs <- function(split,pow){

    Auto_loocv_train <- rsample::training(Auto_loocv_split$splits[[split]])

    Auto_loocv_test <- rsample::testing(Auto_loocv_split$splits[[split]])

    mod <- lm(mpg ~ poly(horsepower,pow),data = Auto_loocv_train)

    broom::augment(mod, newdata = Auto_loocv_test) |>
        select(
            mpg, `.fitted`,`.resid`
        ) |>
            mutate(
                split = split,
                pow = pow
            )

}

pmap(
    list(
        split = rep(c(1:391),10),
        pow = rep(c(1:10),391) |> sort()
    ),
    get_error_obs
) |>
    list_rbind() -> error_obs_tab

error_obs_tab |>
    kableExtra::kable() |>
    kableExtra::kable_styling() |>
    kableExtra::scroll_box(width = '100%', height = '500px')